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近期即将分享的一些代码待续……
tulipsliu
1086 30
2020-12-03
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一些数学公式学习；

公式一：
$$
\begin{aligned}
V_j &= v_j &
X_i &= x_i - q_i x_j &
&= u_j + \sum_{i\ne j} q_i \\
V_i &= v_i - q_i v_j &
X_j &= x_j &
U_i &= u_i
\end{aligned}\tag{1.0.1}
$$

公式二：
$$
\begin{align}
A_1 &= N_0 (\lambda ; \Omega’)
- \phi ( \lambda ; \Omega’) \\
A_2 &= \phi (\lambda ; \Omega’)
\phi (\lambda ; \Omega) \\
\intertext{and finally}
A_3 &= \mathcal{N} (\lambda ; \omega)
\end{align}\tag{1.0.2}

$$

Fomula 3 :
$$
\begin{align}
x^2+y^2 &= z^2 \label{eq:A} \\
x^3+y^3 &= z^3 \notag \\
x^4+y^4 &= r^4 \tag{$*$} \\
x^5+y^5 &= r^5 \tag*{$*$} \\
x^6+y^6 &= r^6 \tag{\ref{eq:A}$’$} \\
A_1 &= N_0 (\lambda ; \Omega’)
- \phi ( \lambda ; \Omega’) \\
A_2 &= \phi (\lambda ; \Omega’)
\, \phi (\lambda ; \Omega)
\tag*{ALSO (\theequation)} \\
A_3 &= \mathcal{N} (\lambda ; \omega)
\end{align}

$$


fomula 4 :
$$
\begin{split}
\lvert I_2 \rvert &= \left\lvert \int_{0}^T \psi(t)
\left\{ u(a, t) - \int_{\gamma(t)}^a \frac{d\theta}{k}
(\theta, t) \int_{a}^\theta c (\xi) u_t (\xi, t) \,d\xi
\right\} dt \right\rvert \\
&\le C_6 \Biggl\lvert
\left\lvert f \int_\Omega \left\lvert
\widetilde{S}^{-1,0}_{a,-} W_2(\Omega, \Gamma_l)
\right\rvert \ \right\rvert
\left\lvert \lvert u \rvert
\overset{\circ}{\to} W_2^{\widetilde{A}} (\Omega; \Gamma_r,T)
\right\rvert \Biggr\rvert
\end{split}\tag{1.0.4}
$$

fomula 5:

$$
\begin{gather} \raisetag{-10pt}
\text{The sign function: \ }
\mathcal{S}(x) = \begin{cases}
-1 & x < 0 \\
0 & x = 0 \\
1 & x>0
\end{cases}
\end{gather}\tag{1.0.5}

$$
fomula 6:
$$
\begin{gather*}
\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix} \quad
\begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix} \\
\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix} \quad
\begin{Bmatrix} 1 & 0 \\ 0 & -1 \end{Bmatrix} \\
\begin{vmatrix} a & b \\ c & d \end{vmatrix} \quad
\begin{Vmatrix} i & 0 \\ 0 & -i \end{Vmatrix}
\end{gather*}\tag{1.0.6}
$$
Equantion 7:
$$
\frac{1}{k} \log_2 c(f)
\quad \tfrac{1}{k} \log_2 c(f) \tag{1.0.7}$$
Text: $ \sqrt{ \frac{1}{k} \log_2 c(f) } \quad
\sqrt{ \dfrac{1}{k} \log_2 c(f) }\, $.
so,
Equantion 8:
$$
\biggl( \mathbf{E}_{y} \int_0^{t_\varepsilon}
L_{x, y^x(s)} \varphi(x)\, ds \biggr)\tag{1.0.8}
$$







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tulipsliu
2020-12-4 07:58:32
```C
library(LaplacesDemon)
### Create Data
J <- 10 #Number of variables
m <- 20 #Number of missings
N <- 50 #Number of records
mu <- runif(J, 0, 100)
sigma <- runif(J, 0, 100)
X <- matrix(0, N, J)
for (j in 1:J) X[,j] <- rnorm(N, mu[j], sigma[j])
### Create Missing Values
M1 <- rep(0, N*J)
M2 <- sample(N*J, m)
M1[M2] <- 1
M <- matrix(M1, N, J)
X <- ifelse(M == 1, NA, X)
### Approximate Bayesian Bootstrap
imp <- ABB(X, K=1)
### Replace Missing Values in X (when K=1)
X.imp <- X
X.imp[which(is.na(X.imp))] <- unlist(imp)
X.imp

```
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tulipsliu
2020-12-4 07:58:52
复制代码
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tulipsliu
2020-12-4 11:32:16
$$X_{t-1} = \left\{\begin{array}{lr}
+ 0.591 + 1.254 X_{t-0}- 0.418 X_{t-1}& Z_t \leq + 3.25\\
+ 2.23 + 1.53 X_{t-0}- 1.24 X_{t-1}& Z_t > + 3.25\\
\end{array}\right.$$
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tulipsliu
2020-12-4 17:30:37
D:/softApp/R/library/RcppEigen/include/Eigen/src/Core/CoreEvaluators.h:99:8:   required from 'struct Eigen::internal::evaluator<const Eigen::Block<const Eigen::Block<const Eigen::Map<const Eigen::Matrix<double, -1, -1, 1, -1, -1>, 0, Eigen::OuterStride<> >, 1, -1, true>, 1, -1, false> >'
   D:/softApp/R/library/RcppEigen/include/Eigen/src/Core/CoreEvaluators.h:269:8:   required from 'struct Eigen::internal::unary_evaluator<Eigen::Transpose<const Eigen::Block<const Eigen::Block<const Eigen::Map<const Eigen::Matrix<double, -1, -1, 1, -1, -1>, 0, Eigen::OuterStride<> >, 1, -1, true>, 1, -1, false> >, Eigen::internal::IndexBased, double>'
D:   D:/softApp/R/library/RcppEigen/include/Eigen/src/Core/CoreEvaluators.h:90:8:   required from 'struct Eigen::internal::evaluator<Eigen::Transpose<const Eigen::Block<const Eigen::Block<const Eigen::Map<const Eigen::Matrix<double, -1, -1, 1, -1, -1>, 0, Eigen::OuterStride<> >, 1, -1, true>, 1, -1, false> > >'
   D:/softApp/R/library/RcppEigen/include/Eigen/src/Core/CoreEvaluators.h:99:8:   required from 'struct Eigen::internal::evaluator<const Eigen::Transpose<const Eigen::Block<const Eigen::Block<const Eigen::Map<const Eigen::Matrix<double, -1, -1, 1, -1, -1>, 0, Eigen::OuterStride<> >, 1, -1, true>, 1, -1, false> > >'
   D:/softApp/R/library/RcppEigen/include/Eigen/src/Core/CoreEvaluators.h:681:51:   required from 'struct Eigen::internal::binary_evaluator<Eigen::CwiseBinaryOp<Eigen::internal::scalar_product_op<double, double>, const Eigen::Transpose<const Eigen::Block<const Eigen::Block<const Eigen::Map<const Eigen::Matrix<double, -1, -1, 1, -1, -1>, 0, Eigen::OuterStride<> >, 1, -1, true>, 1, -1, false> >, const Eigen::Map<const Eigen::Matrix<double, -1, 1>, 0, Eigen::Stride<0, 0> > >, Eigen::internal::IndexBased, Eigen::internal::IndexBased, double, double>'
   D:/softApp/R/library/RcppEigen/include/Eigen/src/Core/CoreEvaluators.h:665:8:   [ skipping 16 instantiation contexts, use -ftemplate-backtrace-limit=0 to disable ]
   D:/softApp/R/library/StanHeaders/include/stan/math/prim/mat/prob/multi_normal_lpdf.hpp:114:45:   required from 'stan::return_type_t<T_x, T_alpha, T_beta> stan::math::multi_normal_lpdf(const T_y&, const T_loc&, const T_covar&) [with bool propto = false; T_y = Eigen::Matrix<double, -1, 1>; T_loc = Eigen::Matrix<double, -1, 1>; T_covar = Eigen::Matrix<double, -1, -1>; stan::return_type_t<T_x, T_alpha, T_beta> = double]'
   D:/softApp/R/library/StanHeaders/include/stan/math/prim/mat/prob/multi_normal_lpdf.hpp:124:34:   required from 'stan::return_type_t<T_x, T_sigma, T_l> stan::math::multi_normal_lpdf(const T_y&, const T_loc&, const T_covar&) [with T_y = Eigen::Matrix<double, -1, 1>; T_loc = Eigen::Matrix<double, -1, 1>; T_covar = Eigen::Matrix<double, -1, -1>; stan::return_type_t<T_x, T_sigma, T_l> = double]'
D:   D:/softApp/R/library/StanHeaders/include/stan/math/prim/mat/prob/multi_normal_log.hpp:26:48:   required from 'stan::return_type_t<T_x, T_sigma, T_l> stan::math::multi_normal_log(const T_y&, const T_loc&, const T_covar&) [with T_y = Eigen::Matrix<double, -1, 1>; T_loc = Eigen::Matrix<double, -1, 1>; T_covar = Eigen::Matrix<double, -1, -1>; stan::return_type_t<T_x, T_sigma, T_l> = double]'
   stan_files/forecastCCC.hpp:1473:53:   required from 'void model_forecastCCC_namespace::model_forecastCCC::write_array(RNG&, std::vector<double>&, std::vector<int>&, std::vector<double>&, bool, bool, std::ostream*) const [with RNG = boost::random::additive_combine_engine<boost::random::linear_congruential_engine<unsigned int, 40014, 0, 2147483563>, boost::random::linear_congruential_engine<unsigned int, 40692, 0, 2147483399> >; std::ostream = std::basic_ostream<char>]'
   D:/softApp/R/library/rstan/include/rstan/stan_fit.hpp:1091:5:   required from 'SEXPREC* rstan::stan_fit<Model, RNG_t>::constrain_pars(SEXP) [with Model = model_forecastCCC_namespace::model_forecastCCC; RNG_t = boost::random::additive_combine_engine<boost::random::linear_congruential_engine<unsigned int, 40014, 0, 2147483563>, boost::random::linear_congruential_engine<unsigned int, 40692, 0, 2147483399> >;
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tulipsliu
2020-12-4 17:31:07
SEXP = SEXPREC*]'
   stan_files/forecastCCC.cc:25:89:   required from here
   D:/softApp/R/library/RcppEigen/include/Eigen/src/Core/CoreEvaluators.h:960:8: warning: ignoring attributes on template argument 'Eigen::internal::packet_traits<double>::type' {aka '__vector(2) double'} [-Wignored-attributes]
   In file included from D:/softApp/R/library/RcppEigen/include/Eigen/Core:434,
                    from D:/softApp/R/library/RcppEigen/include/Eigen/Dense:1,
                    from D:/softApp/R/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13,
                    from D:/softApp/R/library/rstan/include/rstan/rstaninc.hpp:3,
                    from stan_files/forecastCCC.hpp:18,
                    from stan_files/forecastCCC.cc:3:
D:   D:/softApp/R/library/RcppEigen/include/Eigen/src/Core/DenseCoeffsBase.h: In instantiation of 'Eigen::Index Eigen::internal::first_default_aligned(const Eigen::DenseBase<Derived>&) [with Derived = Eigen::Block<const Eigen::CwiseUnaryOp<Eigen::internal::scalar_abs_op<double>, const Eigen::Matrix<double, -1, -1> >, -1, 1, true>; Eigen::Index = long long int]':
   D:/softApp/R/library/RcppEigen/include/Eigen/src/Core/Redux.h:225:63:   required from 'static Eigen::internal::redux_impl<Func, Derived, 3, 0>::Scalar Eigen::internal::redux_impl<Func, Derived, 3, 0>::run(const Derived&, const Func&) [with Func = Eigen::internal::scalar_sum_op<double, double>; Derived = Eigen::internal::redux_evaluator<Eigen::Block<const Eigen::CwiseUnaryOp<Eigen::internal::scalar_abs_op<double>, const Eigen::Matrix<double, -1, -1> >, -1, 1, true> >; Eigen::internal::redux_impl<Func, Derived, 3, 0>::Scalar = double]'
   D:/softApp/R/library/RcppEigen/include/Eigen/src/Core/Redux.h:418:56:   required from 'typename Eigen::internal::traits<T>::Scalar Eigen::DenseBase<Derived>::redux(const Func&) const [with BinaryOp = Eigen::internal::scalar_sum_op<double, double>; Derived = Eigen::Block<const Eigen::CwiseUnaryOp<Eigen::internal::scalar_abs_op<double>, const Eigen::Matrix<double, -1, -1> >, -1, 1, true>; typename Eigen::internal::traits<T>::Scalar = double]'
   D:/softApp/R/library/RcppEigen/include/Eigen/src/Core/Redux.h:453:73:   required from 'typename Eigen::internal::traits<T>::Scalar Eigen::DenseBase<Derived>::sum() const [with Derived = Eigen::Block<const Eigen::CwiseUnaryOp<Eigen::internal::scalar_abs_op<double>, const Eigen::Matrix<double, -1, -1> >, -1, 1, true>; typename Eigen::internal::traits<T>::Scalar = double]'
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